Abstract. Linear time-invariant discrete
digital plant, with no restrictions on the form of the state equation and
the number of controls, is considered. The stabilizing state feedback control
algorithm is developed by Lyapunov's second method leading to the variable
structure system with sliding modes. Essentially the control algorithm
drives the system from an arbitrary initial state to a prescribed so-called
sliding subspace S, in finite time. Inside the sliding subspace S the system
is switched to the sliding mode regime and stay in it for ever.Keywords: Discrete-time digital
system, variable structure systems, Lyapunov's second method, sliding mode